The following pseudocode is an ecient algorithm to evaluate polynomials. This pseudocode shows how to evaluate a_nxⁿ + a_n-1x^n-1 +....+ a₁x¹ + a₀ at x = c. procedure Horner(c; a₀; a₁; a₂; ; ; a_n : real numbers); y := a_n for i := 1 to n y := y c + a_n-i return y {y = a_ncⁿ + a_n-1c^n-1 + : : : + a₁c + a₀} (a) Evaluate x³+ 3x² + x + 1 at x = 2 by working through each step of the algorithm showing the values assigned at each assignment step. (b) Exactly how many multiplications and additions are used by this algorithm to evaluate a polynomial of degree n at x = c? (Do not count additions used to increment the loop variable.